Teaching is not just a matter of instruction given by teachers to their individual students. The progress of science and of knowledge depends in general on the learning that one nation – one group of people – derives from what has been achieved by other nations – and other groups of people. For example, the golden age of Indian mathematics, which changed the face of mathematics in the world, was roughly from the fifth to the twelfth century, and its beginning was directly inspired by what we Indians were learning from work done in Babylon, Greece and Rome. To be sure there was an Indian tradition of analytical thinking, going back much further, on which the stellar outbursts of mathematical work in India from around the fifth century drew, but we learned a lot about theorems and proofs and rigorous mathematical reasoning from the Greeks and the Romans and the Babylonians. There is no shame in learning from others, and then putting what we have learned to good use, and going on to create new knowledge, new understanding, and thrillingly novel ideas and results.
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Learning from others - Let me end with an example. The history of the term “sine” in Trigonometry illustrates how we learn from each other. That trigonometric idea was well developed by Aryabhata, who called it jya-ardha, and sometimes shortened it to jya. The Arab mathematicians, using Aryabhata’s idea, called it “jiba,” which is phonetically close. But jiba is a meaningless sound in Arabic, but jaib, which has the same consonants, is a good Arabic word, and and since the Arabic script does not specify vowels, the later generation of Arab mathematicians used the term jaib, which means a bay or a cove. Then in 1150 when the Italian mathematician, Gherardo of Cremona, translated the word into Latin, he used the Latin word “sinus,” which means a bay or a cove in Latin. And it is from this – the Latin sinus - that the modern trigonometric terms “sine” is derived. In this one word we see the interconnection of three mathematical traditions – Indian, Arabic and European.
- More Here
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Learning from others - Let me end with an example. The history of the term “sine” in Trigonometry illustrates how we learn from each other. That trigonometric idea was well developed by Aryabhata, who called it jya-ardha, and sometimes shortened it to jya. The Arab mathematicians, using Aryabhata’s idea, called it “jiba,” which is phonetically close. But jiba is a meaningless sound in Arabic, but jaib, which has the same consonants, is a good Arabic word, and and since the Arabic script does not specify vowels, the later generation of Arab mathematicians used the term jaib, which means a bay or a cove. Then in 1150 when the Italian mathematician, Gherardo of Cremona, translated the word into Latin, he used the Latin word “sinus,” which means a bay or a cove in Latin. And it is from this – the Latin sinus - that the modern trigonometric terms “sine” is derived. In this one word we see the interconnection of three mathematical traditions – Indian, Arabic and European.
- More Here
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